# Mathematical Proof for Diversity

Last week, Lisa and I joined some friends for a lecture put on by the Santa Fe Institute. SFI is known for its quirkiness, and this was the first of their lectures I had attended, so I didn’t know quite what to expect. The speaker was Scott Page, who is at SFI but also at Michigan. He is a computational economist, using methods like agent-based modeling to study economics and how they impact societies.

Page spoke about diversity and how it plays a role in problem solving and prediction. However, he approached the topic from a mathematical perspective. He began with some anecdotes which “demonstrate” that diversity is good for problem solving, predicting, etc. He told of one story, in particular, from an old English fair in which people were trying to guess the weight of a steer. The average guess was withing 1 pound of the right answer! These kinds of observations are what has led to the formal study of diversity and the role it plays in groups.

The short answer is that diversity often helps. If all of the people in a group are “smart” relative to a problem (that is, they know something about the topic; they are not completely ignorant about it, like a non-mechanic trying to fix a car), then it is better to have a diverse group, including what Page called the “pinhead”, rather than a whole bunch of people who are all the very best, but are all similar. Invariably, in computer models, the diverse group always solves problems better than the “better” group. This is because they have more tools at their disposal, as the pinhead has some tools the genius does not have. By working together, they can solve a wider range of problems than if the group only had geniuses.

Related to this is the predictive quality, and there is actually a mathematical equation relating the error a crowd makes in predictions to the diversity of the crowd. If the diversity is greater, the average prediction of the crowd has a smaller error. This has been demonstrated by looking at expert predictions for, for example, sports (NFL, NBA) drafts, comparing each expert’s pick with the average guess. In almost all cases, each individual expert had more error in their predictions than did the average prediction.

I asked Page about cases where diversity hurts and he pointed out that irreversible processes, such as cooking, are cases were diversity hurts. If I throw chili peppers into the soup, it doesn’t matter what tools you have, you can’t undo what I did. If my peppers ruined the soup, it is ruined no matter how many people are helping. The military, he pointed out, is an interesting case: you want diversity in planning, to come up with the best plan, but you don’t in operations, as you want people to follow the plan already made up. They need to be more single-minded in operations.

Thus, the two adages: “Two heads are better than one” and “Too many cooks spoil the stew” are both right. It is only now, though, that math and science can begin to tell us under which conditions one or the other applies. This is fascinating stuff!

# The Allergies Attack with a Vengence!

Man, last Friday, I was out with some friends, feeling great and then Saturday I woke up feeling like crap. It felt like a minor cold, and, to be honest, that is what I’d hoped it was. I knew allergies were flaring up for other people, but I’d been lucky up til now, not having even a symptom of allergies. But, this year, wham! I have them pretty bad. All thanks to the little guys hidden in the picture. I’d much rather be sick since being sick is a shorter burden. I’ve had allergy symptoms for a week now and they aren’t getting any better yet.

It is weird how these allergies work. I would think they’d be strongest the first time you encounter the pollen and get progressively weaker as you build up a tolerance. But, I’ve been here in Santa Fe for 7 years and never had any problem until now. I hope now I start building some kind of tolerance.

There must be people who never get allergies because otherwise I don’t see how a place like Santa Fe would ever get settled. Maybe it is the 7-year delay that makes it happen. I also wonder if the Native Americans who were here originally got allergies. If so, why did they stay here? I guess most of the year it is worth it, but this week it sure doesn’t feel like it.

I don’t recall anyone I knew when I was a kid in Idaho having problems with seasonal allergies like this. It must be the dryness here that causes them to be stronger in New Mexico. That’s my only guess.

Well, I’ll keep going, hoping it rains soon to wash the air of pollen. But, man, do these allergies suck!

# Thoughts on the death of Captain America

I’m a big comic book fan. Or at least, I used to be. I collected mostly Marvel comics, and mostly X-Men at that, since I was a kid. I’ve stopped reading comics so much, though there are a few great series that I pick up in trade paperback form (including Fables, The Ultimates, Powers, and Astonishing X-Men). While I don’t read all of the comics coming out today, I do keep abreast of what is going on in the two big universes: DC and Marvel.

This week, probably the biggest event to hit comics since the death of Superman happened in the pages of Captain America #25: Captain America, on his way to be arraigned for breaking a registration law, is shot. If you frequent the typical sites for comics news (e.g. Newsarama and The Pulse), you’ll see a lot of outrage and angst over Cap’s death, many posters claiming they’ll give up on comics all together (at least, Marvel comics) and wishing illwill on the creators and editors of Marvel.

It seems that a lot of this vitriol comes from people who haven’t read the issue. Mind you, neither have I. But, from what I’ve read and seen, it seems that the issue is actually very well written and that the current writer, Ed Brubaker, has done a marvelous job on Cap for the last 25 issues. It seems that people aren’t willing to let a major event like this happen, even though it may result in some great stories.

I compare this death with the recent “death” of Kara Thrace on Battlestar Galactica. From what I’ve read on BG spoiler sites, it seems that Starbuck’s death was at least partially due to conflicts between the actor and the producers/writers of the show. This, to me, seems a pointless death. She is killed off only because the actor isn’t going to be part of the show anymore. I mean, of course they have to do it, but in terms of the story, it means that any plots that dealt with her have to be dropped and that any grand vision for her character is no more.

Compare that to Cap’s death. This is determined solely by the writers and editors of the comic; Steve Rogers didn’t decide to stop being Cap. That said, often such events are gimmicks and result in poor story telling. However, in this case, a solid writer is behind the series. And, even if they do bring Cap back, which many see as a foregone conclusion, if it results in great stories, then so be it. Kill Cap.

I personally am not so hung up on continuity, a big deal for many comics fans. I think it would be better if writers focused not on single issues but trade paperback-length stories that weren’t quite as open-ended as the typical comic series. Sure, a lot of great stories come out of the current format, but so does a lot of dreck.

So, while I haven’t been reading Cap, I’m really intrigued by the current story line and am going to get the TPBs of Brubaker’s issues to date. It sounds like one hell of a ride to me.

# Fullmetal Alchemst

I just finished watching the anime series Fullmetal Alchemist, which is based upon a comic book of the same name. It is about two brothers who live in a world where a form of alchemy exists. Specifically, certain people can transmute matter from one form to another. Without spoiling the show, the brothers are trying to find the power to fix their bodies, which they damaged when performing a special transmutation.

Most American cartoons are pretty shallow, being little more than independent 30 minute episodes that really don’t build upon one another. Of course, this isn’t 100% true, as shows like X-Men and Justice League Unlimited had story lines that lasted seasons. However, Fullmetal Alchemist does them one better in creating a world and a story that continues to build upon itself for 50+ episodes. Each episode reveals more richness in the world as the brothers Elric discover more about how alchemy works and the major players in their world.

The story touchs a number of deep subjects, including the costs of war, the atrocities that are committed during war, the nature of truth, the role of science (in this world, alchemy) in society, just to name a few. The brothers, though young (early teens), become quite the philosophers through the course of the show.

There are some things that annoyed me. When trying to display extreme emotions, the art gets a bit more cartoony than I like; it breaks the flow of the rest of the animation, which is more realistic and generally quite good. I also didn’t like that one of the characters, Armstrong, constantly is flexing his muscles for all around to see.

There were also a few things I didn’t understand. I didn’t get the whole point of the character Rose. I didn’t see what she added to the story or was supposed to represent. And I don’t quite get why Japanese animation has characters that look more western. You rarely see Asian characters in western animation, so I’m a bit confused as to why Japanese animators use western characters so much.

Overall, though, I think this is an excellent series with a deep story line and involving characters. I highly recommend it!

# Radiation Effects in Solids

My first book is out! Ok, not exactly. But, I am a co-editor of the “hot new release” (seriously, that is what Amazon is calling it) Radiation Effects in Solids, edited by myself, Kurt Sickafus and Eugene Kotomin. I’m also co-author, with Art Voter, of one of the chapters on Accelerated Molecular Dynamics Methods.

This book grew out of a summer school that Kurt Sickafus held in 2005, I believe, in Erice, Italy. He brought together many experts on radiation effects in solids who gave lectures to the next generation of researchers in the field. The timing couldn’t have been better, as the United States, along with a number of other countries, is reexamining nuclear energy as a crucial component of the nation’s energy portfolio. Since the Carter administration, no new nuclear reactors have been built in the US and, correspondingly, the expertise in areas such as nuclear materials has diminished.